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    • Rectangle triangle problem

      1 September, 1997
      September 1997
      Triangle in rectangle

      If we label the distances AP, PB, CQ and QB as shown above then we can write three equations for the areas of the triangles as follows:

      Equations
      Ratio

      Notice that the two ratios are the same! If we call this ratio r then we can calculate a polynomial for r as follows:

      Polynomial

      Taking the positive root gives us the golden ratio:

      Phi
      • Log in or register to post comments

      Daz

      29 November 2019

      Permalink
      Comment

      For explaining a solution like this one that uses very few variables, it's much easier to read if the variables are named with different letters, but no subscripts.

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